Mechanical model implemented in Matlab/Simulink

4.4.1.1 Dynamic behaviour of the PMSG without damping system

The PMSG when it is coupled to the grid network through a full scale converter has no relative damping. Which is due to the following:

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 The lack of damper windings for the PMSG wind turbine system. On a scenario that the PMSG happens to be connected to a frequency converter, which is the usually is the provider of variable stator frequency which is in accordance to the actual rotor speed, there is never any relative motion between stator and rotor field. Without this relative motion between stator and rotor, a damper winding would not have any impact, since there is no voltage that will be induced in the damper winding.

 The small pole pitch of the multipole generator would cause the damper winding to provide insufficient damping

 Since the PMSG uses permanent magnets it has no field windings, which is incapable of providing sufficient damping either. The system has inadequate damping even if the shaft of the generator is damped. When the system experiences fluctuations, for instance from load changes contributed by wind gust, the PMSG will be involved in exciting oscillations, which are amplified in the system and hence requiring an external damping of the wind turbine system.

Variations of load due to wind gusts or grid faults can excite oscillations in the mechanical part of the wind turbine, which might be insufficiently damped. For this reason of instability, it is essential to represent the mechanical system of the PMSG WTS by means of a two mass model, but when a representation by means of a one mass model is implemented it would diminish such oscillations. Due to the nature of the high number of poles in the generator and it`s large diameter, it raises generator inertia compared to most of the convectional 2 or 4 pole generators. The effective shaft stiffness of a generator is assumed to be reduced by increasing number of poles, sin a manner as follows:

𝐾𝑠ℎ𝑎𝑓𝑡,𝑒𝑓𝑓 =

𝐾𝑠ℎ𝑎𝑓𝑡Ω𝑔𝑒𝑛

𝑆 𝑝

(4.1)

where 𝐾𝑠ℎ𝑎𝑓𝑡,𝑒𝑓𝑓 denotes the effective shaft stiffness, 𝐾𝑠ℎ𝑎𝑓𝑡 is the shaft stiffness in (Nm/rad), S

denotes the rated MVA-base of the generator and p is the number of pole pairs.

From the equation it is clear that any mechanical torsion of the system results in amplified dynamic changes of the electrical rotor angle for a multipole generator. A torsional twist of the shaft connected to a multipole generator has thus a stronger impact on the electrical systems, hence the two mass model makes it ideal to represent a detailed model of the shaft system.

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4.4.1.2 Dynamic behaviour of the PMSG with the external damping system

For a convectional PMSG to be damped from its drive train oscillations an external damping system must be utilised. Some of the ways in which damping can be implemented are to damp the generator as a result of a compliant mounting of the generator [79] which can be provided from the electrical system. For large synchronous generators the damping for speed and rotor angle oscillations is provided by as a result of controlling the generator excitation. For wind applications a similar method is present in [36] where wind turbines with DC excited synchronous generator and a diode rectifier uses the excitation voltage to control and buffer transiently the power flow in the DC-link capacitor. However, the PMSG has a fixed excitation electrical damping is only achievable by utilising a frequency converter. Since the DC-link capacitor serves as a buffer between generator and the grid the Dc-link voltage can be used for damping. The general working principles of such damping and investigation is covered in detail in [76]

The novel SS-PMG or SSG generator topology, in contrast to the PMSG, has damping provision along with other beneficial characteristics integrated into the generator itself as a result of its construction design. As expressed in [33, 21] utilising a radial flux SS-PMG, which has a slip rotor capable of being implemented as a short-circuited wound rotor or as a cage rotor connected to another half coupled with the grid to form a grid-connected PMSG. This grid side of the machine is driven indirectly by the torque from the wind turbine, which is transmitted through the first PMIG stage. The advantage of this back to back connection is that it introduces damping and allows for some rotational speed difference between the turbine and the PM-rotor.

The SS_PMG comprises of two masses namely the turbine and slip rotor combined with the PM-rotor and the grid-connected stator. Even if the connection between the PM-rotor and stator is very lightly damped, it is possible to avoid oscillations in this connection by making it substantially stiffer than the connection between the slip-rotor and the PM-rotor. If the slip-rotor to PM connection is less stiff, then any disturbances will cause an oscillation to develop between these masses. Any such oscillations will be quickly dealt with since the slip-rotor to PM-rotor connection is sufficiently damped. As a result, the SS-PMG will be able to remain connected to the grid in a stable manner, despite torque disturbances from wind gusts and tower shadow effects. Figure 4-9 shows the Simulink implementation for the system, showing the effect of wind speed fluctuation given as a result of the turbine torque fluctuation from stand still till rated torque in per unit system.

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Figure 4-9: Simulink implementation of the complete wind energy system.

Figure 4-10 shows the simulation results of wind speed, generator speed, stator currents and torque production for the cases of when a mechanical drive train is integrated with the PMIG which provides external damping of the system, after a wind speed step change which is represented by a change in turbine torque from standstill to rated torque in per unit after 1 sec. The simulation results illustrate the impact of the damping system, the oscillations of the drive train are supressed effectively when the PMIG is implemented.

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Figure 4-10: Simulation results of wind speed, generator speed, stator currents and torque production for the cases of when a mechanical drive train is integrated with the PMIG.

The simulations in Figure 4-10 illustrate the impact of the damping system. When the wind speed changes no oscillations of any nature are experienced showing a suppressed effectively when the PMIG is treated as part of the drive train.

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